[Music as a] language may be the best we have for explaining what we are like to others in space, with least ambiguity. I would vote for Bach, all of Bach, streamed out into space, over and over again … to put the best possible face on at the beginning of such an acquaintance. We can tell the harder truths later.

All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not.

Cells are required to stick precisely to the point. Any ambiguity, any tendency to wander from the matter at hand, will introduce grave hazards for the cells, and even more for the host in which they live. … There is a theory that the process of aging may be due to the cumulative effect of imprecision, a gradual degrading of information. It is not a system that allows for deviating.

Every rule has its limits, and every concept its ambiguities. Most of all is this true in the science of life, where nothing quite corresponds to our ideas; similar ends are reached by varied means, and no causes are simple.

I believe … that we can still have a genre of scientific books suitable for and accessible alike to professionals and interested laypeople. The concepts of science, in all their richness and ambiguity, can be presented without any compromise, without any simplification counting as distortion, in language accessible to all intelligent people … I hope that this book can be read with profit both in seminars for graduate students and–if the movie stinks and you forgot your sleeping pills–on the businessman’s special to Tokyo.

I think people get it upside down when they say the unambiguous is the reality and the ambiguous is merely uncertainty about what is really unambiguous. Let’s turn it around the other way: the ambiguous is the reality and the unambiguous is merely a special case of it, where we finally manage to pin down some very special aspect.

If we consider that part of the theory of relativity which may nowadays in a sense be regarded as bone fide scientific knowledge, we note two aspects which have a major bearing on this theory. The whole development of the theory turns on the question of whether there are physically preferred states of motion in Nature (physical relativity problem). Also, concepts and distinctions are only admissible to the extent that observable facts can be assigned to them without ambiguity (stipulation that concepts and distinctions should have meaning). This postulate, pertaining to epistemology, proves to be of fundamental importance.

In medicine … beware of ambiguity.

It is the very strangeness of nature that makes science engrossing. That ought to be at the center of science teaching. There are more than seven-times-seven types of ambiguity in science, awaiting analysis. The poetry of Wallace Stevens is crystal-clear alongside the genetic code.

Journalists do not like to report on uncertainties. They would almost rather be wrong than ambiguous.

Most classifications, whether of inanimate objects or of organisms, are hierarchical. There are “higher” and “lower” categories, there are higher and lower ranks. What is usually overlooked is that the use of the term “hierarchy” is ambiguous, and that two fundamentally different kinds of arrangements have been designated as hierarchical. A hierarchy can be either exclusive or inclusive. Military ranks from private, corporal, sergeant, lieutenant, captain, up to general are a typical example of an exclusive hierarchy. A lower rank is not a subdivision of a higher rank; thus, lieutenants are not a subdivision of captains. The scala naturae, which so strongly dominated thinking from the sixteenth to the eighteenth century, is another good illustration of an exclusive hierarchy. Each level of perfection was considered an advance (or degradation) from the next lower (or higher) level in the hierarchy, but did not include it.

Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you’ll never notice the flaws; if you doubt too much you won’t get started. It requires a lovely balance.

On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.

Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.

Suppose that you are in love with a lady on Neptune and that she returns the sentiment. It will be some consolation for the melancholy separation if you can say to yourself at some possibly pre-arranged moment, “She is thinking of me now.” Unfortunately a difficulty has arisen because we have had to abolish Now. There is no absolute Now, but only the various relative Nows, differing according to their reckoning of different observers and covering the whole neutral wedge which at the distance of Neptune is about eight hours thick. She will have to think of you continuously for eight hours on end in order to circumvent the ambiguity “Now.”

There is probably no other science which presents such different appearances to one who cultivates it and to one who does not, as mathematics. To this person it is ancient, venerable, and complete; a body of dry, irrefutable, unambiguous reasoning. To the mathematician, on the other hand, his science is yet in the purple bloom of vigorous youth, everywhere stretching out after the “attainable but unattained” and full of the excitement of nascent thoughts; its logic is beset with ambiguities, and its analytic processes, like Bunyan’s road, have a quagmire on one side and a deep ditch on the other and branch off into innumerable by-paths that end in a wilderness.

This is the element that distinguishes applied science from basic. Surprise is what makes the difference. When you are organized to apply knowledge, set up targets, produce a usable product, you require a high degree of certainty from the outset. All the facts on which you base protocols must be reasonably hard facts with unambiguous meaning. The challenge is to plan the work and organize the workers so that it will come out precisely as predicted. For this, you need centralized authority, elaborately detailed time schedules, and some sort of reward system based on speed and perfection. But most of all you need the intelligible basic facts to begin with, and these must come from basic research. There is no other source. In basic research, everything is just the opposite. What you need at the outset is a high degree of uncertainty; otherwise it isn’t likely to be an important problem. You start with an incomplete roster of facts, characterized by their ambiguity; often the problem consists of discovering the connections between unrelated pieces of information. You must plan experiments on the basis of probability, even bare possibility, rather than certainty.